Mass formula for various generalized weight enumerators of binary self-dual codes

نویسندگان

  • Akihiro Munemasa
  • Michio Ozeki
چکیده

In this paper we give extensions of the mass formula for biweight enumerators and the Jacobi weight enumerators of binary self-dual codes and binary doubly even self-dual codes. For binary doubly even self-dual codes, our formula is expressed in terms of the root system E8 embedded in C4 for biweight enumerators, while the root system D4 is employed for Jacobi weight enumerators. For self-dual codes, the mass formula for biweight enumerators (resp. Jacobi weight enumerators) is controlled by the root system F4 (resp. B2). We show that, in some cases, the mass formula is already sufficient to generate the ring of invariants of a certain finite group. The mass formula for Jacobi weight enumerators can be used to construct Jacobi forms, and we give an explicit example which differ from the Eisenstein– Jacobi series.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Brief Survey of Self-Dual Codes

This report is a survey of self-dual binary codes. We present the fundamental MacWilliams identity and Gleason’s theorem on self-dual binary codes. We also examine the upper bound of minimum weights of self-dual binary codes using the extremal weight enumerator formula. We describe the shadow code of a self-dual code and the restrictions of the weight enumerator of the shadow code. Then using t...

متن کامل

Extension theorems for self-dual codes over rings and new binary self-dual codes

In this work, extension theorems are generalized to self-dual codes over rings and as applications many new binary self-dual extremal codes are found from self-dual codes over F2m + uF2m for m = 1, 2. The duality and distance preserving Gray maps from F4 + uF4 to (F2 + uF2) and F42 are used to obtain self-dual codes whose binary Gray images are [64, 32, 12]-extremal self-dual. An F2 + uF2-exten...

متن کامل

New extremal binary self-dual codes of length 68 via short kharaghani array over f_2 + uf_2

In this work, new construction methods for self-dual codes are given. The methods use the short Kharaghani array and a variation of it. These are applicable to any commutative Frobenius ring. We apply the constructions over the ring F2 + uF2 and self-dual Type I [64, 32, 12]2-codes with various weight enumerators obtained as Gray images. By the use of an extension theorem for self-dual codes we...

متن کامل

On the Existence of Certain Optimal Self-Dual Codes with Lengths Between 74 and 116

The existence of optimal binary self-dual codes is a long-standing research problem. In this paper, we present some results concerning the decomposition of binary self-dual codes with a dihedral automorphism group D2p, where p is a prime. These results are applied to construct new self-dual codes with length 78 or 116. We obtain 16 inequivalent self-dual [78, 39, 14] codes, four of which have n...

متن کامل

Z 2 Z 4 - Additive Formally Self - Dual Codes

We study odd and even Z2Z4 formally self-dual codes. The images of these codes are binary codes whose weight enumerators are that of a formally self-dual code but may not be linear. Three constructions are given for formally self-dual codes and existence theorems are given for codes of each type defined in the paper.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004